Bending Response Research Articles

Response analysis of functionally graded piezoelectric plate resting on elastic foundation under thermo-electro environment

The paper investigates the static, bending and vibration responses of the functionally graded piezoelectric plate (FGPP) resting on the two/three-parameter foundation under a thermo-electro environment. Hamilton’s principles are used with first-order shear deformation theory to obtain the governing equations. They are solved using nine noded interpolation functions with 63 degrees of freedom (DOFs) per element. It is observed that the two-parameter foundation has a shear layer dominant, and the three-parameter foundation has an additional layer of spring that plays a significant role in the static bending and vibrational behavior of the CB/UCB conditions FGPP. The applied electrical voltage and the temperature change affect the static bending, and vibrational results as the rise in temperature lead to the plate’s softening. An increase in voltage leads to a reduction in the stiffness of the plate. Also, Sg-law significantly influences the dimensionless frequency, center deflection, and axial stress compared to other laws.

On thermo-mechanical bending response of porous functionally graded sandwich plates via a simple integral plate model

On thermo-mechanical bending response of porous functionally graded sandwich plates via a simple integral plate model

Bending and buckling analysis of functionally graded Timoshenko nanobeam using Two-Phase Local/Nonlocal piezoelectric integral model

Previous studies indicate that nonlocal piezoelectric differential model would lead to an inconsistent bending response of Euler-Bernoulli nanobeam. In this paper, static bending and elastic buckling of functionally graded piezoelectric (FGP) Timoshenko nanobeam are studied through two-phase local/nonlocal piezoelectric integral model. The differential governing equations and standard boundary conditions are derived on the basis of the principle of minimum potential energy. The relations between general strain and nonlocal stress components are expressed as integral forms and then transformed equivalently into differential forms with constitutive boundary conditions. Several nominal variables are introduced to simplify the mathematical formulation. It shows that Timoshenko nanobeam based on purely nonlocal piezoelectric integral model would lead to ill-posed mathematical model and inconsistent size-dependent response with and without considering constitutive boundary conditions, respectively. The general differential quadrature method is applied to obtain the numerical results for bending deflections and buckling loads. The influence of nonlocal parameters, boundary conditions, functionally graded index and buckling order on the bending deflections and buckling loads is investigated numerically. A consistent softening response is obtained.

Mechanical behavior of concrete pipes with erosion voids and the effectiveness evaluation of the polyurethane grouting

Research on pipes ringed by erosion voids is mainly concerned with circumferential mechanical behavior but ignores longitudinal bending responses induced by the relative motion of the pipe joints at voids. There has been limited innovative experimental investigation into pipe behavior that assesses the effectiveness of polyurethane (PU) grouting in rehabilitating erosion voids. Mechanical behavior tests of concrete pipes of intact, with an erosion void at the invert, and PU grouted were performed using a self-developed large-scale disaster testing system, and the measured results were numerically verified. Results show that the peaks of the positive and negative longitudinal bending moments of the intact pipes and pipes with a void at the invert appear at SgL2 and SgR2, SgL3 and SgR3, respectively, and the positive longitudinal bending moment is about 1.6–3.0 times higher than the negative ones. Voids at the invert have a significant effect on the longitudinal bending moments of the pipe segments located on the adjacent sides of the void. The longitudinal bending moments of the pipes with different void widths decrease with the increase of void width at SgL1 and SgR1 and increase with the increase of void width at SgL2 and SgR2, SgL3 and SgR3. The longitudinal bending moments of the pipes with different void lengths increase with the increase of void length in the whole longitudinal length. The circumferential bending moments at the bell-and-spigot decrease as the void width and void length increase. The maximum increases in the vertical displacements and maximum shear displacements of the pipes with different void widths and void lengths are 63–150% and 150–221%, 225–325%, and 325–550%, respectively, compared with the intact pipes. The rehabilitation efficiencies of the longitudinal and circumferential bending moments and the vertical displacement ranged from 85–93% and 85–94%.

Free and forced small flexural vibrations of slightly curved slender composite beams with interlayer slip

This paper presents a beam theory for analyzing the dynamic bending response of slender slightly curved composite beams whose layers are flexibly connected and therefore subject to interlayer slip. The equations of motion and boundary conditions are derived using Hamilton’s principle, assuming separately for each layer the applicability of Euler–Bernoulli theory and a linear elastic relationship between the interlayer slip and the shear traction. For the problem of a three-layer slightly curved single-span beam with symmetric layer arrangement and soft-hinged bearings, analytical expressions for the natural frequencies and the eigenfunctions are derived. For the arbitrarily supported two-layer beam, on the other hand, a numerical solution scheme of the combined initial boundary value problem is presented. Several examples show how important it is to consider even very small deviations from the straight beam axis in the prediction of the dynamic response for slender beams with interlayer slip, in particular when all supports are immovable. The comparison of the beam solutions with the results of much more expensive FE analyses based on plane stress elasticity proves the accuracy of the presented theory.

Selective fiber Bragg grating inscription in multicore fiber by femtosecond laser and phase mask

An effective and stable method for selective fiber Bragg gratings (FBGs) inscription in multicore fibers (MCFs) using a femtosecond laser and phase mask is presented. The nonlinear photoluminescence imaging technique is adopted for visually displaying the position of the femtosecond laser focus-line inside the MCF, which helps to guarantee that the laser focal-line is precisely positioned in a preset fiber core during the inscription process. FBGs with different wavelengths are successfully inscribed into each core of a seven-core fiber (SCF). The FBGs show good consistency with a side-mode suppression ratio more than 27 dB. In addition, the largest difference of the peak intensity in the reflection spectrum between different FBGs is less than 1.4 dB and the 3-dB bandwidth for the seven FBGs is less than 0.3 nm. Confirmatory experiments show that the FBGs in the SCF have perfect directional bending response. This method provides an effective scheme for selective FBGs inscription in a multicore fiber.

Analysis of sandwich structures with corrugated and spiderweb-inspired cores for aerospace applications

The bending response of laminated composite sandwich structures developed for aircraft flaps is analyzed, in two parts. In the first part, the carbon fiber reinforced plastic (CFRP) and Aluminium 6061 based single-sided trapezoidal corrugated core sandwich panels are considered. The developed design is observed to withstand higher loads and exhibits higher flexural stiffness as compared to the similar corrugated geometries in the literature. The core design is iteratively modified to maximize the contact points between the core and panel in contact with the lift forces. The structure is treated as a cantilever, thus, representing the boundary conditions of aircraft flaps. The influence of ply-orientation, stacking sequences of face sheets, and panel thickness on the bending response are studied. As a result, an optimized sandwich composite structure with two times more stiffness and 40% lower stress levels as compared to the initial design is arrived. Furthermore, dynamic analysis is performed considering sinusoidally varying load along the space and time. In the second part, a novel bio-inspired spiderweb core design for the aircraft flap is developed. The stiffness of the bio-mimicked sandwich composite structures is observed to be better than the optimized corrugated core structures proposed in the first part. The influence of scaling and patterning the geometry is also investigated. The simulations are further extended to study the influence of hail impact on the sandwich structures with optimized corrugated and spiderweb cores to estimate the maximum induced stresses and peak forces. Finally, the corrugated design is replaced with the proposed spiderweb-based core design while preserving the optimal fiber orientation and ply-thickness developed in the first part.

Temperature-Insensitive Two-Dimensional Vector Bending Sensor Based on Fabry-Pérot Interferometer Incorporating a Seven-Core Fiber

We proposed and experimentally demonstrated a temperature-insensitive two-dimensional (2D) vector bending sensor on the basis of Fabry-Pérot Interferometer (FPI). The sensor is fabricated by splicing a section of silica capillary optical fiber (COF) between a trench-assisted seven-core fiber (SCF) and a multimode fiber (MMF). For orientation angle from 0° to 360°, the vector bending responses of six outer-core FPIs were studied at a step of 30°. From experimental results, the proposed sensor exhibits strong bending-direction dependence, and the maximum sensitivity is 200.6 pm/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−1</sup> . The curvature magnitude and orientation angle can be reconstructed through the dip wavelength shifts of any two off-diagonal outer-core FPIs. Hence, there are 12 various combinations from six outer-core FPIs, and the average value can be taken in multiple reconstructions to develop exact 2D vector bending measurement. For curvature magnitude and orientation angle reconstructed, the average relative error is 6.2% and 3.3%, respectively. In addition, experiments verified the proposed sensor is insensitive to ambient temperature changes.

On the static, vibration, and transient responses of micro-plates made of materials with different microstructures

In the present paper, for the first time, theoretical analysis for static, dynamic, and transient responses of micro-plates made of different materials were comprehensively performed. The constitutive relations of analyzed materials satisfy assumptions of the modified couple stress theory. Additionally, values of length scale parameters of studied materials are taken from well-established experimental results presented in the literature. A generalized model of micro-plates made from Cu, Ni, Ti, and Epoxy satisfies assumptions of Reissner–Mindlin plate theory. The formulated generalized boundary value problem is solved by analytical and the radial basis function finite difference (RBF-FD) methods. A convergence study is performed to show the advantages and correctness of the obtained numerical solution. The meshless numerical method is easy to implement and it provides accurate results that are in excellent agreement with analytical solutions. Effects of material parameters, boundary conditions, and assumptions of classical and the modified couple stress theory on the static bending, free vibration and transient responses of micro-plates are presented and discussed.

Smart carboxymethyl cellulose/polythiophene hydrogel for electrically driven soft actuators: Physical and thermal properties and electroactive performances

AbstractNovel electroactive hydrogels were fabricated from carboxymethyl cellulose (CMC) biopolymer incorporated with conductive polythiophene (PTh). The PTh particles dispersed uniformly in the CMC matrix providing higher mechanical properties and thermal stability. The formulation CMC/PTh6 (6%wt PTh) gave the highest tensile strength and elongation at break (0.9456 ± 0.0017 MPa and 123.0398 ± 7.0606%, respectively). The bending response of the hydrogels under an applied electric field was studied in terms of bending angle and bending sensitivity. Under an electric field strength of 100 V mm−1, CMC/PTh10 (10%wt PTh) showed the highest bending angle (52.245 ± 6.054°) while neat CMC gave the lowest bending angle (33.753 ± 8.116°). The bending behavior upon the application of an electric field of the CMC/PTh hydrogels occurs from the polarization of Na+ and H+ in the CMC matrix and S+ in PTh.

A non-polynomial framework for describing the bending response of a multi-scale composite initially stressed disk

The present study deals with axisymmetric circular/annular disks made of three-phase multi-scale hybrid laminated nanocomposite under distributed static loadings. The structure is placed on Winkler-Pasternak substrate with friction effects. Initial stress is also considered in the composite structure. The mathematical model is prepared using three-dimensional elasticity theory (3D-elasticity theory). The derived differential equations are solved by employing the semi-analytical method of state-space-based differential quadrature method (SS-DQM) to obtain the stress and displacement fields of the composite structure. In the numerical analyses, a comprehensive parametric study is performed to observe the effects of some geometrical and physical parameters on bending characteristics of composite circular/annular disks.

Axial-bending coupling vibration characteristics of a rotating blade with breathing crack

Blade crack is one of the most common blade failures of rotating machines which may lead to catastrophic accidents. Although many nonlinear vibrations of breathing crack have been investigated, there are few reports on the axial-bending coupling vibration caused by crack. With the aim of providing physical insight into the mechanisms of axis-bending coupling due to crack, a novel axial-bending coupled breathing crack model (ABCBCM) for the rotating blade is proposed in this study. The proposed ABCBCM is analytically formulated based on the Timoshenko beam theory and Castigliano’s principle, and validated by comparing the natural and dynamic characteristics with the finite element model (FEM) and experimental tests. In addition, the effects of boundary conditions (rotational speed), crack parameters (crack depth and crack location) and loading conditions (excitation load) on the vibration characteristics of the cracked blade are investigated. The results indicate that the blade axial response is more sensitive to the nonlinearity caused by the breathing crack than the bending response; the axial-bending coupling caused by the crack changes the equilibrium position of the axial and bending displacement; the phase portrait of axial response and the orbit of axial-bending displacement are effective methods to detect breathing crack; and the axial displacement amplitude ratio and the axial acceleration amplitude ratio also are valuable indicators to estimate the severity of the blade crack. The proposed model can provide valuable insights for fault diagnosis and safety monitoring of cracked blade.

Construction and Live Load Behavior of a Skewed Steel I-Girder Bridge

As part of a long-term monitoring project, a two-span continuous steel I-girder bridge (skewed 41° with seat-type abutments) was instrumented and evaluated in the field during construction and after the bridge was in service. This paper discusses data from when the first stage (of a three-stage sequence) was constructed and initially opened to traffic. Girders and cross-frames were instrumented with strain gauges using a data acquisition system with a high sampling frequency (up to 20 Hz). Data collection began just before deck placement, and a series of live load tests was then conducted on the completed Stage I (half of the bridge) using a loaded truck. Three-dimensional finite element analyses were carried out to provide enhanced understanding of bridge behavior. Good agreement was observed between the numerical simulation results and the field monitoring data for both deck placement and live load testing. A slight inconsistency between numerical simulation and field measurement data at one girder section and an adjacent cross-frame indicated an unexpected local site condition, which was confirmed through a targeted field inspection. Live load distribution factors used during design conservatively overestimate bridge girder strong-axis bending response under live load (by around 50%). Maximum flange lateral bending stresses of 6.3 MPa (0.9 kips per square inch [ksi]) and 2.5 MPa (0.4 ksi) were observed during deck placement and truck tests, respectively. In addition, out-of-plane response of 10.6 MPa (1.5 ksi) was observed at girder web plates under concrete dead load.

Comparative studies between Semi-analytical and shear deformation theories for functionally graded beam under bending

In this paper, the bending response of functionally graded (FG) beam using three different approaches. viz. semi-analytical, higher-order shear and normal deformation theory (HOSNT), and trigonometric shear deformation theory (TSDT) under transverse loading conditions has been investigated. The boundary value problem (BVP) of the HOSNT and TSDT is derived using principle of virtual work whereas semi-analytical approach consist of formation of two-point BVP along the beam depth. All three models satisfy zero shear stress conditions at the top and bottom surfaces of the beam. The material properties of the FG beam vary across the thickness direction according to the power-law distribution. Aluminium-zirconia and aluminium-alumina are two types of compositions used to create FG beams. For comparison purpose, the authors have generated results for semi-analytical and HOSNT, being not available in the published literature. The numerical results are compared with previously published solutions to assess the correctness and effectiveness of the three models.

A computationally efficient C0 continuous finite element model for thermo-mechanical analysis of cross-ply and angle-ply composite plates in non-polynomial axiomatic framework

In the present article, the thermo-mechanical bending response of multi-layered composite plates is investigated in the framework of inverse-hyperbolic shear deformation theory using a generalized finite element model. The mathematical development is carried out under the assumptions of linear structural kinematics for the materials following generalized Hooke’s law. Energy-based finite element formulation and the principle of minimum potential energy are employed to develop the finite element governing equations. A computationally efficient C0 continuous finite element formulation is developed to examine the response of laminated composites subjected to constant, linear, and non-linear temperature change. Numerical analyses are carried out for composite laminates considering various lamination sequences (cross-ply as well as angle-ply), boundary conditions, loading conditions, span-thickness ratio, etc. The present results are compared with the existing analytical and numerical results and their agreement is observed. The effect of fiber orientation angle on bending response is analyzed to enable the optimal design of laminated composite structures under thermo-mechanical loading.

Bending Response of Lattice Structure Filled Tubes under Transverse Loading

Thin-walled tubes are widely used as passive energy-absorbing structures in a variety of industries. These structures are typically filled with lightweight materials to improve their energy absorption capabilities. At this point, additive manufacturing technology offers a great chance researchers for the production of novel filler structures to increase the crashworthiness performance of thin-walled tubes. In the current work, additive manufacturable body-centered cubic (BCC) lattice structures are suggested as filling materials for thin-walled tubes, and the bending response of these structures is investigated under transverse loads via a finite element modeling approach. The aspect ratio and strut diameter are considered as design parameters, and three-point bending simulations are conducted to understand the transverse load bearing behaviors of the structures. Different loading offsets are also taken into account for three-point bending simulations. The numerical results revealed that the BCC lattice structures used as filler materials significantly increase the energy absorption performance of thin-walled tubes due to synergetic interactions. In particular, the simulation results revealed that the hybrid tubes can absorb up to 84% more energy than the empty tubes, while the crush force efficiency of these structures is up to 42% higher compared to the empty tubes. The present study also showed that the transverse crushing characteristics of tubes can be considerably improved by suitable selection of the design parameters. These primary outcomes reveal that the proposed lattice structures can be considered as a potential alternative to traditional filler materials for enhancing the bending response of thin-walled tubes under transverse loading.

Biaxial bending design of solid steel storage rack uprights in global buckling

This study aims at investigating the biaxial bending capacity of cold-formed steel (CFS) storage rack uprights undergoing global (lateral-torsional) buckling. A previously published and validated biaxial bending numerical model for local and distortional buckling of CFS rack uprights is initially validated in this paper for global buckling and then used to evaluate and analyse the biaxial bending response of nine unperforated upright cross-sections. Nine biaxial bending configurations were considered per cross-section. Results show that a nonlinear interactive relationship typically governs the biaxial bending of the studied uprights. This relationship is discussed and analysed for different cross-sectional slenderness. The numerical capacities are compared with both the classical DSM predictions and the use of inelastic reserve capacity in the DSM. Results show that the classical DSM equations underestimate the biaxial bending capacity by up to 55% but results in better predictions when the inelastic reserve capacity is considered. Finally, an extended range of inelastic reserve strength for global buckling is proposed which results in a 14% improvement of the DSM predictions. The appropriate form of the DSM to estimate the global biaxial bending capacity of unperforated cold-formed steel storage rack uprights is discussed.

Pre- and Post-Failure Experimental Bending Analysis of Glass Elements Coated by Aged Anti-Shatter Safety Films

The main goal of Anti-Shatter Films (ASFs) applications for structural glass is to create a barrier able to keep together fragments and minimize risk after any impulsive or static load that could lead glass to cracking. The influence of ASF properties on the flexural strength of coated glass elements is thus a relevant topic for safe design purposes, but still little investigated. To this aim, an experimental material investigation is presented in this paper, in order to achieve a good knowledge of common ASFs from a chemical point of view. Moreover, the deterioration of mechanical and adhesion characteristics for ASF samples subjected to different environmental conditions and accelerated ageing is also investigated, so as to simulate the effects of long-term exposure to high humidity (HU) or high temperature (HT). An experimental campaign carried out on 20 small scale ASF-coated glass specimens is finally presented, based on a three-point bending (3PB) test setup. The out-of-plane bending response of unaged or aged samples is performed by taking into account two different displacement-rate levels, to assess their performance and bending capacity under steady-static or impulsive loads. In both cases, the attention is given to the characterization of elastic and post-failure performances. Finally, support for the interpretation of experimental outcomes is derived from a simplified theoretical model of composite beam with partial connection, in order to estimate the shear stiffness of ASF adhesive components in the elastic stage.

Anchorage of shear reinforcement in beams and slabs

Anchorage of shear reinforcement, such as links or stirrups, can be performed by providing hooks, bends or heads at their ends, by welding transverse reinforcement or by closing open stirrups with pins. Hooks and bends, also used to enhance the anchorage of flexural reinforcement at the end regions of beams and slabs, have often been preferred because of their simple and cost-effective production. Such anchorages present nevertheless several peculiarities that shall be accounted for. They are relatively sensitive to their detailing (mandrel diameter, length of the tail segment between bar end and bent region) as well as to the cracking state of the surrounding concrete. Also, brittle failures can occur due to spalling of the concrete cover in case of bars near to a free surface.The anchorage with hooks and bends is currently still widely designed according to old detailing rules, based on the results of tests performed in many cases with materials whose properties are significantly different than those of nowadays. Also, no mechanical models are available for a consistent verification and detailing, acknowledging the different potential failure modes and their interaction with the surrounding concrete. In an effort to provide a consistent approach to its design and verification, this paper presents an investigation addressed at understanding the mechanical response and performance of bend and hook anchorages. To that aim, the results of an experimental programme performed with state-of-the-art instrumentation are introduced. By means of analysis of Digital Image Correlation and Fibre-Optic Measurements, the complete transfer of forces is analysed under different circumstances. On that basis, a consistent mechanical model is developed and validated, also reproducing a large variety of tests found in the literature. The paper introduces eventually several practical considerations on the activation of shear reinforcement in beams, and the level of performance required at its anchorages.

Nonlinear bending analysis of variable thickness multi-directional functionally graded plates based on isogeometric analysis

In this study, the nonlinear bending behavior of multi-directional functionally graded plates with variable thickness is investigated. To this regard, the governing equation of the plate problem is developed based on the principle of virtual work, while the third-order shear deformation plate theory proposed by Reddy is employed to describe the kinematic relations. The geometrical nonlinearity is taken into account by adopting the von Kármán’s assumptions for nonlinear problems with small strains and moderate rotations. The plates investigated in this study are assumed to be made from two different material constituents, whose volume fractions vary spatially within the plate domain. The effective material properties are calculated based on the mixture approach. The Isogeometric Analysis approach is used as a numerical method to solve the governing equations. NURBS basis functions are used as interpolation functions for geometrical modeling and discretization procedure, where the C 1-continuity requirement is meet efficiently. Various numerical examples are conducted to validate the accuracy of the proposed approach and investigate the influences of geometrical and material factors on the nonlinear bending responses of the plates.